Question: Simplify the following expression: $q = \dfrac{3z^2 + 6z - 105}{z + 7} $
Answer: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $3$ , so we can rewrite the expression: $ q =\dfrac{3(z^2 + 2z - 35)}{z + 7} $ Then we factor the remaining polynomial: $z^2 + {2}z {-35} $ ${7} {-5} = {2}$ ${7} \times {-5} = {-35}$ $ (z + {7}) (z {-5}) $ This gives us a factored expression: $\dfrac{3(z + {7}) (z {-5})}{z + 7}$ We can divide the numerator and denominator by $(z - 7)$ on condition that $z \neq -7$ Therefore $q = 3(z - 5); z \neq -7$